1. Field of the Invention
The invention relates to electronic circuits, and more particularly, to generating a constant reference voltage having Nth order temperature compensation.
2. Description of the Prior Art
Bandgap voltage reference circuits are widely used in various applications in order to provide a stable voltage reference over a temperature range. The bandgap voltage reference circuit operates on the principle of compensating the negative temperature coefficient of a base-emitter junction voltage, VBE, with the positive temperature coefficient of the thermal voltage VT, with VT being equal to kT/q. Typically, the variation of VBE with temperature is approximately 1.5 mV/° C., while VT is approximately +0.086 mV/° C. These terms are combined to generate the bandgap voltage, VBG:
                              V          BG                =                                            K              1                        ⁢                          V              BE                                +                                    K              2                        ⁢                          V              T                                                          Eq        .                                  ⁢                  (          1          )                    where K1 and K2 are proportionality constants to ensure that the positive and negative thermal factors cancel one another, and, optionally, to scale the bandgap voltage to accommodate application requirements.
FIG. 1 is a circuit diagram showing a typical bandgap voltage reference circuit 100. The bandgap voltage reference circuit 100 includes PMOS transistors M1, M2 and M3, bipolar transistors Q1 (having emitter area KA) and Q2 (having emitter area A), resistors R0, R1, R2 and R3, and an operational amplifier (Op-amp) 101. Please note that here, in FIG. 1, the resistors R1 and R2 are of the same value. Transistors Q1 and Q2 conduct substantially equal currents. Because the ratio of the emitter areas of transistors Q1 and Q2 is K:1, a . VBE, of substantially VTIn(K), is produced across resistor R0, providing a proportional-to-absolute-temperature current. The Op-amp 101 forces the voltages at nodes V1 and V2 to be equal, thereby causing currents to flow in resistors R1 and R2 which are proportional to VBE and providing a complementary-to-absolute-temperature current. The resulting current through transistors M1 and M2 is thus compensated in accordance with Equation (1). The compensated current is mirrored to transistor M3 to generate the output voltage Vout.
Specifically, in the bandgap reference circuit 100 of FIG. 1, the output voltage VOUT is defined by Equation (2):
                                          V            OUT                    =                                                    R3                R1                            ⁢                              V                BE2                                      +                                          R3                R0                            ⁢                              V                T                            ⁢                              ln                ⁡                                  (                  K                  )                                                                    ,                            Eq        .                                  ⁢                  (          2          )                    where VBE2 is the base-emitter voltage of transistor Q2 and K is the area ratio of transistors Q1 and Q2. Comparing Equation (2) with Equation (1), it is clear that the values of resistors R0, R1 and R3, and the emitter areas of transistors Q1 and Q2 are selected to provide the desired proportionality constants K1 and K2. For any area ratio of transistors Q1 and Q2, it can be shown using Equation (2) that when the resistor values are selected to ensure the positive and negative thermal factors canceling one another, the bandgap reference circuit 100 generates a constant reference voltage VOUT.
However, this constant reference voltage VOUT is only accurate at a specific center temperature. As the temperature of the bandgap reference circuit 100 deviates from the center temperature, there is a significant voltage change in the reference voltage VOUT. For example, over a temperature range from −40° C. to +100° C., a voltage change of approximately 1 mV is typical.